An isosceles right triangle is a 45°-45°-90° triangle. 45°-45°-90° triangles' hypotenuses are always equal to their leg length times the square root of two.
For 45°-45°-90° triangles:
Leg = x
Hypotenuse = x√(2)
The length of the hypotenuse is given (6√(2)), so we can easily find the length of its legs. If we divide the hypotenuse by √(2), we are left with 6. This is the leg length.
To find the area of the triangle (and thus the area of the square), use the formula for area of a triangle, A = bh/2. Our b, base, is 6, and our h, height, is also 6. Plug these values in accordingly and solve.
A = 6 * 6/2
A = 36/2
A = 18
The area of the triangle (and that of the square) is 18 units squared.
Answer:
The area of the square is 18 units².
h) 18